We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Gamma-convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local, non-convex stored energy of inverse strain, augmented by small interfacial energy, formulated in terms of the inverse-strain gradient. They predict spontaneous fracture with exact crack-opening discontinuities, without the use of damage (phase) fields or pre-existing cracks; crack faces are endowed with a thin layer of surface energy. The models obtained herewith inherit the same properties, except that surface energy is now concentrated at the crack faces. Accordingly, we construct energy-minimizing configurations. For a composite bar with a breakable layer, our results predict a pattern of equally spaced cracks whose number is given as an increasing function of applied load.

翻译：本文通过逆变形方法推导了一维脆性断裂的尖锐界面模型。采用Gamma收敛的方法获得先前提出模型的奇异极限。这些模型以逆应变梯度为变量，构建了包含局部非凸逆应变存储能及小界面能的能量泛函，能够在不引入损伤（相）场或预存裂纹的条件下，准确预测具有裂纹张开间断的自发断裂行为；裂纹面被赋予薄层表面能。本文所得模型继承相同特性，但表面能现集中于裂纹面。据此，我们构造了能量极小化构型。对于含可断裂层的复合材料杆件，模型预测出等间距裂纹分布模式，其数量随外加载荷单调递增。